, Volume 151, Issue 3, pp 611-664

Homotopy equivalences of p-completed classifying spaces of finite groups

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Abstract.

We study homotopy equivalences of p-completions of classifying spaces of finite groups. To each finite group G and each prime p, we associate a finite category ℒ p c (G) with the following properties. Two p-completed classifying spaces BG p and BG p have the same homotopy type if and only if the associated categories ℒ p c (G) and ℒ p c (G’) are equivalent. Furthermore, the topological monoid Aut(BG p ) of self equivalences is determined by the self equivalences of the associated category ℒ p c (G).

Oblatum 5-VII-2001 & 28-VIII-2002¶Published online: 8 November 2002
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ID="*"C. Broto is partially supported by DGICYT grant PB97–0203.
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ID="**"R. Levi is partially supported by EPSRC grant GR/M7831.
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ID="***"B. Oliver is partially supported by UMR 7539 of the CNRS.